Question: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}3x+2y &= 4 \\ -8x+2y &= 2\end{align*}$
Explanation: Begin by moving the $x$ -term in the second equation to the right side of the equation. $2y = 8x+2$ Divide both sides by $2$ to isolate $y$ $y = {4x + 1}$ Substitute this expression for $y$ in the first equation. $3x+2({4x + 1}) = 4$ $3x + 8x + 2 = 4$ Simplify by combining terms, then solve for $x$ $11x + 2 = 4$ $11x = 2$ $x = \dfrac{2}{11}$ Substitute $\dfrac{2}{11}$ for $x$ back into the top equation. $3( \dfrac{2}{11})+2y = 4$ $\dfrac{6}{11}+2y = 4$ $2y = \dfrac{38}{11}$ $y = \dfrac{19}{11}$ The solution is $\enspace x = \dfrac{2}{11}, \enspace y = \dfrac{19}{11}$.